The field of mesh simplification aims at rearranging and pruning the vertices of a mesh in order to reduce the number of arcs in the mesh and thus allowing faster computations on meshes, better compression ratios, and overall better algorithm efficiency. A complete review of remeshing algorithms can be found in Alliez et al., Recent Advances in remeshing of Surfaces, Shape Analysis and Structuring, 2008.
Wang et al., Content-Aware Geometry Image Resizing, in Computer Graphics International 2010 (CGI 2010) Short Papers, Singapore, 2010 discloses Content aware image Resizing algorithms that are applied to a geometry image in order to reduce its size and its contents in a non-uniform manner allowing to lay emphasis on parts of the mesh with the most details while removing less noticeable vertices. The concept of Geometry Image was discussed by Gu et al. in Gu et al., Geometry Images, SIGGRAPH, 2002, in which mesh parameterization is conducted for the creation of a 2D structure named Geometry image. In the Geometry Image for each vertex xyz in the model is associated an RGB value coding the xyz values. This very efficient scheme conducts to the creation of a regularized mesh that is imposed by the grid structure of the image.
However, the method of Wang et al suffers at least the following two drawbacks. First, the content aware image retargeting algorithms used do not create smooth transformations of the image thus creating visible artefacts in the mesh when its reduction is large, e.g. spurious vertices. Noon-smooth deformations create local maxima in the derivatives of the Geometry Image, thus rendering further compression much more difficult. For instance, as the image is reduced the compression ratio of this image lowers; this is due to the creation of artifacts in the continuity of the image and its derivatives.
Second, the algorithms used are specifically created for images, thus completely disregarding the fact that the final end product is a simplified mesh. For instance, preserving the boundary regularity of the geometry image may be not relevant when performing a mesh simplification.
Within this context, there is still a need for an improved method for the simplification of a three-dimensional mesh. In particular, the method should selectively reduce the geometry image in a smooth and regular fashion.